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Binary decomposition and coding schemes for the nonnegative and peak-constrained additive white Gaussian noise channel Bahanshal, Sarah Ahmad


We consider the design of practical capacity-approaching coding schemes for the peak-constrained intensity modulation with direct detection (IM/DD) channel. This channel is used to model point-to-point optical wireless communication. We first introduce the vector binary channel (VBC), which decomposes the peak-constrained continuous IM/DD channel into a set of N bit-pipes. The decomposition is almost capacity-preserving, i.e., lossless, when the model’s parameters are tuned well. This holds since the decomposition represents binary addition with carryover properly; eliminating information loss. Furthermore, a method for converting the Gaussian noise random variable into N Bernoulli random variables is proposed to be used in the VBC. Additionally, we propose five practical coding schemes for the VBC model. Among the five proposed schemes, the best coding scheme in terms of achievable rates is the State-Aware Coding, which approaches the peak-constrained IM/DD channel capacity at moderate to high signal-to-noise ratio (SNR). This scheme uses coding for a channel with state, and makes use of the previously decoded bit-pipes as a state for the current decoding operation. Moreover, the Independent Coding scheme, which encodes over each bit-pipe independently and decodes independently and sequentially while subtracting the carryover, is found to be 0.2 nats away from capacity. All five proposed schemes are shown to have a maximum of 1 nats gap to capacity, and could be easily realized in practice by a binary-input channel capacity-achieving code, such as a polar code.

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